Virtual contraction and passivity based control of nonlinear mechanical systems: trajectory tracking and group coordination

Recent technological developments of smart industries (or industry 4.0), smart cities, precision systems, among others, require a high level of process automation where the motion control systems (or servo-systems) are key for the fulfillment and good performance of the overall process tasks. The aforementioned motion control systems are complex nonlinear engineering systems due to their highly coupled, multivariable and multi-domain nature. Under the right assumptions, these servo systems can be modeled as nonlinear mechanical systems for control design purposes. Therefore, the study of advanced control techniques for (networked) nonlinear mechanical systems is a pertinent subject of research.

In this dissertation constructive control methods for solving the trajectory tracking and group coordination problems of nonlinear mechanical systems are proposed. These design methods are based on the concepts of virtual systems, contraction analysis and passivity. Several practical cases are considered in the present work, the tracking control design for fully-actuated mechanical systems, flexible-joints robots and marine craft in the port-Hamiltonian (pH) framework; and the group coordination of networked mechanical systems in the Euler-Lagrange (EL) framework. Both energy based modeling approaches are suitable for control design purposes, since these allows us to have a clear physical understanding of the control schemes.
The performance of the closed-loop fully-actuated system and of flexible joint robot are evaluated experimentally on a robot platform of two degrees of freedom; whereas the performance of the closed-loop marine craft and of the network of mechanical systems are evaluated via simulations.